Semiparametric fractional imputation using Gaussian mixture models for handling multivariate missing data

Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the parametric fractional imputation of \cite{kim2011parametric} may be subject to bias under model misspecification. In this paper, we propose a novel semiparametric fractional imputation method using Gaussian mixture models. The proposed method is computationally efficient and leads to robust estimation. The proposed method is further extended to incorporate the categorical auxiliary information. The asymptotic model consistency and $\sqrt{n}$- consistency of the semiparametric fractional imputation estimator are also established. Some simulation studies are presented to check the finite sample performance of the proposed method.Comment: 23 pages, 2 figure

Loss of Quantum Coherence and Positivity of Energy Density in Semiclassical Quantum Gravity

In the semiclassical quantum gravity derived from the Wheeler-DeWitt equation, the energy density of a matter field loses quantum coherence due to the induced gauge potential from the parametric interaction with gravity in a non-static spacetime. It is further shown that the energy density takes only positive values and makes superposition principle hold true. By studying a minimal massive scalar field in a FRW spacetime background, we illustrate the positivity of energy density and obtain the classical Hamiltonian of a complex field from the energy density in coherent states.Comment: RevTex, 6 pages, no figure

Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase

The Moody-Shapere-Wilczek's adiabatic effective Hamiltonian and Lagrangian method is developed further into the matrix effective Hamiltonian (MEH) and Lagrangian (MEL) approach to a parameter-dependent quantum system. The matrix-operator approach formulated in the product integral (PI) provides not only a method to find the wave function efficiently in the MEH approach but also higher order corrections to the effective action systematically in the MEL approach, a la the Magnus expansion and the Kubo cumulant expansion. A coupled quantum system of a light particle of a harmonic oscillator is worked out, and as a by-product, a new kind of gauge potential (Berry's connection) is found even for nondegenerate cases (real eigenfunctions). Moreover, in the PI formulation the holonomy of the induced gauge potential is related to Schlesinger's exact formula for the gauge field tensor. A superadiabatic expansion is also constructed, and a generalized Dykhne formula, depending on the contour integrals of the homotopy class of complex degenerate points, is rephrased in the PI formulation.Comment: RevTex 17 pages, no figure; added Refs. [28-46] published after 1992; to be published in J. Korean Phys. So

Bayesian Sparse Propensity Score Estimation for Unit Nonresponse

Nonresponse weighting adjustment using propensity score is a popular method for handling unit nonresponse. However, including all available auxiliary variables into the propensity model can lead to inefficient and inconsistent estimation, especially with high-dimensional covariates. In this paper, a new Bayesian method using the Spike-and-Slab prior is proposed for sparse propensity score estimation. The proposed method is not based on any model assumption on the outcome variable and is computationally efficient. Instead of doing model selection and parameter estimation separately as in many frequentist methods, the proposed method simultaneously selects the sparse response probability model and provides consistent parameter estimation. Some asymptotic properties of the proposed method are presented. The efficiency of this sparse propensity score estimator is further improved by incorporating related auxiliary variables from the full sample. The finite-sample performance of the proposed method is investigated in two limited simulation studies, including a partially simulated real data example from the Korean Labor and Income Panel Survey.Comment: 38 pages, 3 table

One-Parameter Gaussian State of Anharmonic Oscillator: Nonlinear Realization of Bogoliubov Transformation

We find a one-parameter Gaussian state for an anharmonic oscillator with quadratic and quartic terms, which depends on the energy expectation value. For the weak coupling constant, the Gaussian state is a squeezed state of the vacuum state. However, for the strong coupling constant, the Gaussian state represents a different kind of condensation of bosonic particles through a nonlinear Bogoliubov transformation of the vacuum state.Comment: 8 pages, RevTex, no figure

Renormalization of Black Hole Entropy

We review the renormalization of one-loop effective action for gravity coupled to a scalar field and that of the Bekenstein-Hawking entropy of a black hole plus the statistical entropy of the scalar field. It is found that the total entropy of the black hole's geometric entropy and the statistical entropy yields the renormalized Bekenstein-Hawking area-law of black hole entropy only for even dimensional Reissner-N\"{o}rdstrom (Schwarzschild) black holes. We discuss the problem of the microscopic origin of black hole entropy in connection with the renormalization of black hole entropy.Comment: Proceedings of the 5th Korean-Italian Symposium on Relativistic Astrophysics, Seoul Korea, 1997; 10 pages, RevTe

An approximate Bayesian inference on propensity score estimation under unit nonresponse

Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the non- response weighting adjustment is complicated because the effect of estimating the propensity model parameter needs to be incorporated. In this paper, we propose an approximate Bayesian approach to handle unit nonresponse with parametric model assumptions on the response probability, but without model assumptions for the outcome variable. The proposed Bayesian method is cal- ibrated to the frequentist inference in that the credible region obtained from the posterior distribution asymptotically matches to the frequentist confidence interval obtained from the Taylor linearization method. Unlike the frequentist approach, however, the proposed method does not involve Taylor linearization. The proposed method can be extended to handle over-identified cases in which there are more estimating equations than the parameters. Besides, the proposed method can also be modified to handle nonignorable nonresponse. Results from two simulation studies confirm the validity of the proposed methods, which are then applied to data from a Korean longitudinal survey

An approximate Bayesian inference on propensity score estimation under unit nonresponse

Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the non- response weighting adjustment is complicated because the effect of estimating the propensity model parameter needs to be incorporated. In this paper, we propose an approximate Bayesian approach to handle unit nonresponse with parametric model assumptions on the response probability, but without model assumptions for the outcome variable. The proposed Bayesian method is cal- ibrated to the frequentist inference in that the credible region obtained from the posterior distribution asymptotically matches to the frequentist confidence interval obtained from the Taylor linearization method. Unlike the frequentist approach, however, the proposed method does not involve Taylor linearization. The proposed method can be extended to handle over-identified cases in which there are more estimating equations than the parameters. Besides, the proposed method can also be modified to handle nonignorable nonresponse. Results from two simulation studies confirm the validity of the proposed methods, which are then applied to data from a Korean longitudinal survey

The Effect of Brick Walls on the Black Hole Radiation

In order to understand the physical effect of the brick wall boundary condition, we compute the distribution of the zero-point energy of the massless scalar fields minimally coupled to the Schwarzschild and Reissner-Nordstr\"{o}m black hole backgrounds. We find that the black hole radiation spectrum depends on the positions of the brick wall and the observer, and reveals the interference effect due to the reflected field by the brick wall.Comment: 8 pages, no figures, Revte

Semiclassical Limit and Time in Quantum Cosmology

We propose a method to recover the time variable and the classical evolution of the Universe from the minisuperspace wave function of the Wheeler-DeWitt equation. Defining a Hamilton-Jacobi characteristic function $W$ as the imaginary part of the $\ln \Psi$ we can recover the classical solution, and quantum corrections. The key idea is to let the energy of the Wheeler-DeWitt equation vanish only after the semiclassical limit is taken.Comment: RevTex, 7 pages, no figures; the methodology is clarified and references adde